A covariance RLS lattice for adaptive filtering

"Covariance" or "unwindowed" Recursive Least Squares (RLS) adaptive algorithms are useful in applications where the input data cannot be assumed to be zero before application of these algorithms. Equivalently, the initial data inside the filter is nonzero before the very first iteration of the covariance RLS algorithm. Several computationally efficient covariance RLS algorithms have appeared in both lattice and transversal-filter form. However, the existing lattice algorithms have two problems that are remedied by the newly presented covariance-lattice RLS algorithm of this paper: First, the new algorithm permits a non-zero initial condition on the filter response (in addition to permitting the non-zero data), which is not permitted by any modification of the previous covariance-lattice RLS algorithms. Second, the new covariance-lattice algorithm can begin processing data at any point in time without the need for "warning" the algorithm (N-1) time samples in advance, as is required in all of the previous covariance-lattice algorithms. The new covariance lattice algorithm has an entirely different set of internal recursions in comparison to the previous algorithms, mainly because the order and number of terms in the sum of squared errors are unrelated during the computations comprising the new algorithm. An added benefit is that the new covariance-lattice RLS algorithm is also slightly more computationally efficient than the previous covariance-lattice RLS algorithms.